Question

show that the square of an not the integer can be the form 6q+1 and 6q+3 for some integer q

Answer 1

let a be any +ve integer and b=6 so by Euclid division lemma or algorithm a=bq+r ie a=6q+r where 0=r=0,1,2,3,4,5 fill this value in a=6q+r u will get any +be odd integer is of th form 6q+1,6q+3,6q+5